All reports by Author Jonathan Mosheiff:

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TR24-093
| 16th May 2024
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Omar Alrabiah, Jesse Goodman, Jonathan Mosheiff, Joao Ribeiro#### Low-Degree Polynomials Are Good Extractors

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TR24-091
| 14th May 2024
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Dean Doron, Jonathan Mosheiff, Mary Wootters#### When Do Low-Rate Concatenated Codes Approach The Gilbert--Varshamov Bound?

Revisions: 1

Omar Alrabiah, Jesse Goodman, Jonathan Mosheiff, Joao Ribeiro

We prove that random low-degree polynomials (over $\mathbb{F}_2$) are unbiased, in an extremely general sense. That is, we show that random low-degree polynomials are good randomness extractors for a wide class of distributions. Prior to our work, such results were only known for the small families of (1) uniform sources, ... more >>>

Dean Doron, Jonathan Mosheiff, Mary Wootters

The Gilbert--Varshamov (GV) bound is a classical existential result in coding theory. It implies that a random linear binary code of rate $\varepsilon^2$ has relative distance at least $\frac{1}{2} - O(\varepsilon)$ with high probability. However, it is a major challenge to construct explicit codes with similar parameters.

One hope to ... more >>>